Rodgers was 34 of 42 for a career-high 480 yards and four touchdowns, and James Jones had 11 catches for a career-best 178 yards in a 38-20 victory Sunday.
Robert Griffin III threw for 320 yards and three touchdowns for the Redskins, but most of that came in the second half with the
Packers ahead by three TDs.
James Starks had 132 yards rushing and a touchdown. Randall Cobb added nine catches for 128 yards and a 35-yard touchdown on a crossing route for a 10-0 lead on a fourth-and-3 play in the first quarter to make it 10-0.
Rodgers added touchdown passes to Jordy Nelson and Jermichael Finley in the second quarter. The Packers led 24-0 at the half, and Rodgers already had 335 yards passing.
Green Bay (1-1) bounced back after a season-opening loss at San Francisco.
The Redskins (0-2) will need to regroup again after getting off to a slow start for a second straight week.
Last week, the Redskins fell behind 26-7 at halftime before rallying in the second half in a 33-27 loss to the Eagles.
Griffin, in the second game of his much-anticipated return from right knee surgery, looked OK but didn't resemble the quarterback who confounded defenses last year.
The Packers' defense threw a couple of different wrinkles, including a sack on a blitz by reserve cornerback Davon House.
Griffin's most memorable play of the first half might have been when his helmet flew off while being tackled by Green Bay linebackers Clay Matthews and A.J. Hawk.
Griffin finished 26 of 40 for 320 yards and three touchdowns, and carried four times for a yard.
The Redskins got on the board after Griffin connected with receiver Pierre Garcon for a 6-yard touchdown pass. The play held up on review after the official ruled Garcon extended his hand over the goal line with the ball before running out of bounds.
The score made it 31-7 with 4:15 left in the third quarter.
Garcon finished with eight catches for 143 yards against a Packers defense playing again without injured safety Morgan Burnett. Alfred Morris had 13 carries for 107 yards for Washington.
The Redskins also had a couple of other good drives into Green Bay territory. But they were foiled by a missed 50-yard field goal by John Potter.
The Packers' Mike Neal intercepted Griffin after receiver Josh Morgan lost his grip on the ball after being hit by Matthews.
Early on, it was the Redskins administering the big hits.
Rodgers was sacked on consecutive plays inside the 18 by Ryan Kerrigan on the game's first series, and the Packers had to settle for a field goal. He was sacked on the first play of his next series by Brian Orapko.
Things looked shaky again on the third series after facing fourth down at the Redskins 35. But Rodgers found Cobb for the score and the Packers' offense got on track.
Starks had the first 100-yard rushing game for a Packer since Brandon Jackson ran for 115 at Washington on Oct. 10, 2010.
Losing starting running back Eddie Lacy to a concussion didn't slow down the running game. The rookie from Alabama got knocked out after an apparent helmet-to-helmet hit by Redskins safety Brandon Meriweather.
Making his season debut after sitting out last week with a groin injury, Meriweather left the game with a concussion after another apparent helmet-to-helmet hit at the sideline on Starks in the second quarter.